Smoothing Estimation of Stochastic Processes. Part I. Change of Initial Condition Formulae.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Recently a great amount of attention has been focused on various algorithms for solving the smoothing problem of linear estimation theory. This work is the first part of a two part investigation of these algorithms. In Part I it is shown how change of initial condition CIC or partitioning formulae hold in a very general setting the CIC problem is shown to involve fixed rank perturbation in matrix inversion. In Part II the nature of the two-filter algorithms is explored by providing a simple derivation that shows to what extent the formulae hold generally and so reveals exactly how a wide sense Markovian assumption is necessary for their full utility. The remainder of the paper is structured as follows. Section I contains a discussion of CIC formulae for discrete observations. Section II concerns CIC formulae for continuous observations actually the formulae are the same. Section III discusses the relation with other work.
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